Timing that cannot lie

1. static long timedSum(int n) — time a loop summing 1..n with nanoTime; return the elapsed NANOS. Verify the sum equals (long) n * (n + 1) / 2 and throw IllegalStateException if it does not (defeat dead-code elimination by consuming the result). 2. static long warmMedianSum(int n, int rounds) — for each of rounds rounds: time the same sum, convert to microseconds, collect; return the MEDIAN of the rounds (sort, take the middle). Warmup is inside: run the sum 2_000 times untimed before measuring. 3. static boolean nanoIsMonotonic() — read nanoTime 1_000 times; return true iff no read was less than its predecessor (strictly: never a NEGATIVE step).

Difficulty: advanced